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Courbes elliptiques sur un anneau et applications cryptographiques

Abstract : The goal of this thesis is to study cryptographic applications of elliptic curves over the ring Fp["], with Fp a finite field of prime order p and with the relation "2 = 0. In a first time, we describe these curves defined over a ring. Then, we study the algorithmic properties by proposing eective implementations for representing the elements and the group law. Finally, we study some of their cryptographic properties, with the description of : an attack of the elliptic discrete logarithm problem (over a finite field) using these curves ; a cryptosystem à la ElGamal over these curves. We study its security properties
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Submitted on : Friday, July 3, 2009 - 10:49:27 AM
Last modification on : Monday, October 12, 2020 - 10:27:24 AM
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  • HAL Id : tel-00401449, version 1



Marie Virat. Courbes elliptiques sur un anneau et applications cryptographiques. Mathématiques [math]. Université Nice Sophia Antipolis, 2009. Français. ⟨tel-00401449⟩



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